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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Quantum State and Gate Verification with Minimum Settings
最小设置 量子态 门验证
2023/4/14
Efficient verification of quantum states and gates is crucial to the development of quantum technologies. Although the sample complexities of quantum state verification and quantum gate verification h...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Simultaneous Optimal Transport
优化运输 矢量值度量 Wasserstein距离概念
2023/4/14
We propose a general framework of mass transport between vector-valued measures, which will be called simultaneous mass transport. The new framework is motivated by the need to transport resources of ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：非线性随机薛定谔方程的拟周期解
非线性 随机薛定谔方程 拟周期解 安德森模型
2023/4/14
假设离散的安德森模型（一类离散随机薛定谔算子）满足安德森局部化. 与 Weimin Wang 合作，我们证明了一个非线性版本，即非线性随机薛定谔方程存在大量关于时间的拟周期解.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A Squared Smoothing Newton Method for Semidefinite Programming
半定规划 平方平滑 牛顿方法
2023/4/14
This paper proposes a squared smoothing Newton method via the Huber smoothing function for solving semidefinite programming problems (SDPs). We first study the fundamental properties of the matrix-val...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Approximate Envy-freeness in Indivisible Resource Allocation with Budget Constraints
预算约束 不可分割 资源分配 近似无嫉妒
2023/4/14
We study the fair allocation of indivisible resources under knapsack constraints, where a set of items with varied costs and values are to be allocated to a group of agents. Each agent has a budget co...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Rigidity of non-compact static domains in hyperbolic space via positive mass theorems
正质量定理 双曲空间 非紧致 静域刚性
2023/4/14
We single out a notion of staticity which applies to any domain in hyperbolic space whose boundary is a non-compact totally umbilical hypersurface. For (time-symmetric) initial data sets modeled at in...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Pandora Box Problem with Nonobligatory Inspection: Hardness and Approximation Scheme
潘多拉盒问题 非强制性检查 硬度 近似方案
2023/4/14
Weitzman (1979) introduced the Pandora Box problem as a model for sequential search with inspection costs, and gave an elegant index-based policy that attains provably optimal expected payoff. In vari...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：马氏过程的集中不等式
马氏过程 集中不等式 真实均值 随机算法
2023/4/14
这个报告的主题是马氏过程观察量的经验均值趋于真实均值的集中不等式，或者说随机算法的错误概率的绝对估计。我将介绍与集中不等式等价的“运费vs Fisher信息量”不等式，以及怎样使用Poincare或log-Sobolev不等式，与最优传输，熵这些工具去证明“运费vs Fisher信息量”不等式。作为应用例子，我将介绍高维分布Gibbs算法的错误概率绝对估计。
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Mixed-binary Convex Quadratic Optimization and Its Applications in Inference with Sparsity
二元凸 二次优化 稀疏推理
2023/4/14
Sparsity is a naturally occurring characteristic in many real-world applications including signal denoising, outlier detection, and finance. On one hand, sparsity assumption allows people to tackle in...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Quantum Inequalities and Their Extremisers
量子不等式 极端值 量子对称性
2023/4/14
In this talk, we shall present a series of inequalities for quantum symmetries such as Hausdorff-Young inequalities, Young's inequalities, uncertainty principles, sumset estimation and entropic inequa...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Extension of Kahler currents
Kahler-currents 扩展 解析奇点
2023/4/14
In this lecture I will talk about Collins-Tosatti's proof on the extension of Kahler currents with analytic singularities.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Global and Local Convergence-Rate Analysis of an Inexact Newton Augmented Lagrangian Method for Zero-One Composite Optimization
零一复合优化 不精确 牛顿增强拉格朗日方法 收敛率分析
2023/4/14
Zero-One Composite Optimization (0/1-COP) is a prototype of nonsmooth, non- convex optimization problems and it has attracted much attention recently. Augmented Lagrangian Method (ALM) has stood out a...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On a two dimensional nonlocal shallow-water model
二维 非局部 浅水模型 三维欧拉系统
2023/4/14
In this talk, we first review some related progresses on one dimensional shallow water models. Then we introduce the derivation of a new nonlocal shallow water model from the 3D Euler system with free...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Two Approaches towards elliptic cohomology
椭圆 上同调 两种方法
2023/4/14
An elliptic cohomology theory is an even periodic multiplicative generalized cohomology theory whose associated formal group is the formal completion of an elliptic curve. It is at the intersection of...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Fairness Criteria for Allocating Indivisible Chores: Connections and Efficiencies
分配 不可分割杂务 公平标准
2023/4/14
We study several fairness notions in allocating indivisible chores (i.e., items with non-positive utilities) to agents, who have additive and submodular cost functions. The fairness criteria we are co...